46 
HANDBOOK OF ACOUSTICS. 





The vibration numbers of the upper or lower octaves of these notes, are of course at once obtained by doubling or halving them.
It will be noticed that a scale may be constructed on any vibration number as a foundation. The only reason for selecting 288 was, to avoid fractions of a vibration and so simplify the calculations. As another example let us take d = 200. Proceeding in the same way as before, but tabulating at once, for the sake of brevity, we get 







We may now adopt the reverse process, that is, from the vibration numbers, obtain the vibration ratios. For example, using the first scale, we find that the vibration number of t is to that of n as 540 : 360, that is (dividing each by 180, for the purpose of simplifying) as 3 : 2 ; or more concisely

